The critical radius in sampling-based motion planning

Wednesday, November 1st, 2017, 16:10

Schreiber 309

The Critical Radius in Sampling-Based Motion Planning

Kiril Solovey, TAU

Abstract:

Motion planning is a fundamental problem in robotics: allowing
autonomous robots to efficiently navigate in environments cluttered with
obstacles. Sampling-based algorithms, which were first described two
decades ago, have made a great impact on the field of robotics by
providing simple but highly-effective tools for motion planning. These
techniques aim to capture the structure of the problem by randomly
sampling robot configurations and connecting nearby samples, to form
discrete graphs which approximate the robot's range of movements.

In
this talk I will describe a new result concerning the theoretical
asymptotic guarantees of sampling-based planners, which significantly
improves upon the celebrated work of Karaman and Frazzoli (2011).
Particularly, we prove that the number of neighbors considered for
connection to each sample can be reduced from O(log n) (where n is the
number of samples) to only O(1), without sacrificing asymptotic
completeness or optimality. Continuum percolation theory plays an
important role in our proofs.